Exceptional $\mathfrak{g}_2$ deformations and gauge symmetries

TL;DR

This paper introduces a formalism for deforming the exceptional Lie algebra g2 using Clifford algebra and octonions, revealing subalgebras akin to SU(3) gauge symmetry relevant to QCD.

Contribution

It generalizes g2 applications through Clifford algebra and octonions, uncovering SU(3)-like subalgebras within g2 for the first time.

Findings

Deformation of g2 via Clifford algebra and octonions.

Identification of SU(3)-like subalgebras within g2.

Framework connects exceptional algebra to gauge symmetries.

Abstract

Deformed $\mathfrak{g}_2$ exceptional applications are introduced via the Clifford algebra-parametrized formalism. Using the products between multivectors of $\cl_{0,7}$, the Clifford algebra over the metric vector space $\RR^{0,7}$, and octonions, resulting in an octonion, we generalize the exceptional Lie algebra $\mathfrak{g}_2$ applications, also associated with the transformation rules for bosonic and fermionic fields on the 7-sphere $S^7$. The emergence of $SU(3)$-like subalgebras within the exceptional Lie algebra $\mathfrak{g}_2$ provides an algebraic framework reminiscent of the $SU(3)$ gauge symmetry of QCD.